A Precise Determination of Top Quark Electro-Weak Couplings at the ILC
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IFIC/13-06 LAL 13-265 A precise determination of top quark electro-weak couplingsp at the ILC operating at s = 500 GeV M.S. Amjad1, M. Boronat2, T. Frisson1, I. Garc´ıaGarc´ıa2, R. P¨oschl∗1, E. Ros2, F. Richard1,2, J. Rou¨en´e1, P. Ruiz Femenia2 and M. Vos2 1 LAL, CNRS/IN2P3, Universit´eParis Sud, F-91898 Orsay CEDEX, FRANCE 2IFIC, Universitat de Valencia CSIC, c/ Catedr´aticoJos´eBeltr´an,2 46980 Paterna, SPAIN September 10, 2018 Abstract Top quark production in the process e+e− ! tt at a future linear electron positron collider with polarised beams is a powerful tool to determine indirectly the scale of new physics. The presented study, based on a detailed simulation p of the ILD detector concept, assumes a centre-of-mass energy of s = 500 GeV and a luminosity of L = 500 fb−1 equality shared between the incoming beam polarisations of Pe−;+ = ±0:8; ∓0:3. Events are selected in which the top pair decays semi-leptonically. The study comprises the cross sections, the forward- backward asymmetry and the slope of the helicity angle asymmetry. The vector, axial vector and tensorial CP conserving couplings are separately determined for the photon and the Z0 component. The sensitivity to new physics would arXiv:1307.8102v1 [hep-ex] 30 Jul 2013 be dramatically improved with respect to what is expected from LHC for elec- troweak couplings. 1 Introduction The main goal of current and future machines at the energy frontier is to under- stand the nature of electro-weak symmetry breaking. This symmetry breaking can be ∗Corresponding author: [email protected] 1 generated by the existence of a new strong sector, inspired by QCD, that may man- ifest itself at energies of around 1 TeV. In all realisations of the new strong sector, as for example Randall-Sundrum models [1] or compositeness models [2], Standard Model fields would couple to the new sector with a strength that is proportional to their mass. For this and other reasons, the t quark is expected to be a window to any new physics at the TeV energy scale. New physics will modify the electro-weak ttX vertex described in the Standard Model by Vector and Axial vector couplings V and A to the vector bosons X = γ; Z0. Generally speaking, an e+e− linear collider (LC) can measure t quark electro- weak couplings at the % level. In contrast to the situation at hadron colliders, the leading-order pair production process e+e− ! tt goes directly through the ttZ0 and ttγ vertices. There is no concurrent QCD production of t quark pairs, which increases greatly the potential for a clean measurement. In the literature there a various ways to describe the current at the ttX vertex. Ref. [3] uses: ttX 2 X 2 X 2 (q − q)µ X 2 X 2 Γµ (k ; q; q) = ie γµ Fe1V (k ) + γ5Fe1A(k ) + Fe2V (k ) + γ5Fe2A(k ) : 2mt (1) with k2 being the four momentum of the exchanged boson and q and q the four vectors of the t and t quark. Further γµ with µ = 0; ::; 3 are the Dirac matrices describing vector currents and γ5 = iγ0γ1γ2γ3 is the Dirac matrix allowing to introduce an axial vector current into the theory Applying the Gordon identity to the vector and axial vector currents in Eq.1 the parametrisation of the ttX vertex can be written as: ttX 2 X 2 X 2 σµν µ X 2 X 2 Γµ (k ; q; q) = −ie γµ F1V (k ) + γ5F1A(k ) + (q + q) iF2V (k ) + γ5F2A(k ) ; 2mt (2) i X X with σµν = 2 (γµγν − γνγµ). The couplings or form factors Fei and Fi appearing in Eqs.1 and2 are related via X X X X X X X X X Fe1V = − F1V + F2V ; Fe2V = F2V ; Fe1A = −F1A ; Fe2A = −iF2A : (3) Within the Standard Model the Fi have the following values: γ;SM 2 γ;SM Z;SM 1 8 2 Z;SM 1 F1V = − ;F1A = 0;F1V = − 1 − sw ;F1A = ; (4) 3 4swcw 3 4swcw with sw and cw being the sine and the cosine of the Weinberg angle θW . All the expressions above are given at Born level. Throughout the article no γ attempt will be made to go beyond that level. The coupling F2V is related via 2 γ F2V = Qt(g − 2)=2 to the anomalous magnetic moment (g − 2) with Qt being the electrical charge of the t quark. The coupling F2A is related to the dipole moment d = (e=2mt)F2A(0) that violates the combined Charge and Parity symmetry CP . Due to the γ=Z0 interference the t pair production is sensitive to the sign of the individual form factors. This is in contrast to couplings of t quarks to γ and Z0 individually where the form factors enter only quadratically. The authors of [4] use LEP data to Z set indirect constraints on the electric form factors F1V;A. These limits are sufficient Z Z γ;Z to exclude an ambiguity for F1A but not for F1V . In [4] also rough estimates for jF2V j are given. Today, the most advanced proposal for a linear collider is the International Linear Collider, ILC [5], which can operate at centre-of-mass energies between the Z0 pole to 1 TeV. The ILC provides an ideal environment to measure thesep couplings. The tt pairs would be copiously produced, several 100,000 events at s = 500 GeV for an integrated luminosity of 500 fb−1. It is possible to almost entirely eliminate the background from other Standard Model processes. The ILC will allow for polarised electron and positron beams. With the use of polarised beams, t and t quarks oriented toward different angular regions in the detector are enriched in left-handed or right- handed t quark helicity [6]. This means that the experiments can independently access the couplings of left- and right-handed chiral parts of the t quark wave function to the Z0 boson and the photon. In principle, the measurement of the cross section t and forward-backward asymmetry AFB for two different polarisation settings allows extracting both, the photon and Z0 couplings of the t quark for each helicity state. This study introduces the angle of the decay lepton in semi-leptonic decays of the tt in the rest frame of the t quark. This angle will be called the helicity angle. The slope of the resulting angular distribution is a measure for the fraction of t quarks in left-handed helicity state, tL and right-handed helicity state, tR, in a given sample. There are therefore six independent observables • The cross section; t • The forward backward asymmetry AFB; • The slope of the distribution of the helicity angle; for two beam polarisations. For the extraction of the six CP conserving form factors 0 defined for the Z and the photon, F1V ;F1A and F2V , the following observations have to be taken into account: Close to the tt threshold the observables depend always on the sum F1V + F2V . Therefore a full disentangling of the form factors will be imprecise for energies below about 1 TeV. Hence, in the present study either the four form factors F1V;A are varied simultaneously, while the two F2V are kept at their 3 Standard Model values or vice versa. Throughout this article the CP violating form X factors F2A will be kept at their Standard Model values. This article is organised as follows. After this introduction the relations between the observables and the form factors are outlined before the experimental environment and the used data samples will be introduced. After that the selection of semi- leptonic decays of the tt pair will be presented and the selection efficiencies will be t given. The determination of AFB will be followed by the extraction of the slope of the distribution of the helicity angle. Potential systematic effects from experiment and theory uncertainties will be outlined. Finally the six CP conserving form factors will be extracted as explained above. This study goes therefore beyond earlier studies published in [7,8], 2 Top quark production at the ILC The dominant source of top quark production at a 500 GeV e+e− collider is electro- weak production. The Born-level diagram is presented in Figure 1(a). The decay of the top quarks proceeds predominantly through t ! W ±b. The subsequent decays of the W ± bosons to a charged lepton and a neutrino or a quark- anti-quark pair lead to a six-fermion final state. The study presented in this article focuses on the 'lepton+jets' final state l±νbbq0q. (a) tt pair production (b) Single top production Figure 1: Four diagrams that contribute to the e+e− ! lνbbq0q production: (a) Born-level tt pair production, (b) box diagram higher-order contribution to the same process (c) single top production (d) triple gauge boson production. Several other Standard Model processes give rise to the same final state. The most important source is single-top production through the process e+e− ! WW ∗ ! 4 W tb ! l±νbbq0q. One of the diagrams contributing to this process is presented in Figure 1(b). Another relevant source is the Z0WW production. Due to the coupling of initial state electrons or positrons to to W bosons both sources contribute nearly exclusively in a configuration with left handed polarised electron beams and right handed polarised positron beams. In that case single-top and Z0WW production would yield a production rate of order 10% and 5%, respectively, of that of the pair production diagram of Fig- ure 1(a).